Step 1:
The given inequality
$3(2-x) \geq 2(1-x)$
=> $ 6-3x \geq 2-2x$
adding $2x$ on both sides of inequality.
=> $ 6-3x +2x \geq 2-2x+2x$
=> $ 6-x \leq 2$
adding $-6$ on both sides of inequality
=> $6-x -6 \geq 2-6$
$-x \geq -4$
Multiplying by a negative number -1 on both sides
$x \leq 4$
Step 2:
All real number less than and equal to 4 satisfy the given inequality .
The solution set is $(-\infty, 4]$
Hence B is the correct answer.